Going back to the original question, you can wear anything as long as you are comfortable, especially starting out. Cycling specific shoes and clipless pedals become imporatnt as your milage and speed increases, especially if you move up to a road bike.
I used to be very active in a local cycling club. The slow and easy ride category which consisted of about half hybrids had about 50% of the riders in athletic house and platform pedals. The next highest ride class had more road bikes and 3/4th of riders with cycling specific shoes. This proportion increases as the classes move up in ride distances and speed until you reach the top where 100% have clipless pedals.